A number line, also called a printer's key, is the row of numbers on a copyright page that records which printing a book is. Printers set the full row for the first printing and remove the lowest number at each reprint, so the lowest number left is the printing.
How to spot it
Look near the foot of the copyright page for a row such as "10 9 8 7 6 5 4 3 2 1". Rows can run in any order: descending, ascending or alternating, like "1 3 5 7 9 10 8 6 4 2", which stays centred as numbers are removed. Some lines include year codes, such as "73 72 71 70", where the lowest year is the year of printing. Letters work the same way, with A as the first printing.
What it does to value
A line that still includes a 1 usually means a first printing, which is what collectors pay for. A 2 or higher means a later printing, usually worth much less. There are exceptions: Random House, for example, long started its first printings at 2, and marked them "First Edition" instead, so the publisher's convention matters.
Type your line into the number line decoder for an instant reading, or read number lines explained for the full rules.